Question

Red light of wavelength 633 nm from a helium-neon laser passes through a slit 0.405 mm wide. The diffraction pattern is observed on a screen 3.30 m away. Define the width of a bright fringe as the distance between the minima on either side.

(a) What is the width of the central bright fringe?
mm

(b) What is the width of the first bright fringe on either side of the central one?
mm

Answer 1

Wavelength of the light, $\lambda= 633nm$

Width of the slits,

Distance of slits from Scree,

a). The first minimum is located at

   $sin \theta_1= \frac{\lambda}{a}= \frac{633 \times 10^{-9}}{0.405 \times 10^{-3}}$

   $\theta_1= 0.0895^\circ$

Then distance of central bright fringe on one side of center is

   $y_1=d tan \theta_1= 3.30tan (0.0895^\circ)= 5.15 \times 10^{-3}m= 5.15mm$

Then width of central bright fringe on both sides of center will be

$w_o= 2y_1=2(5.15 \times 10^{-3})m= 10.3 \times 10^{-3}m= 10.3mm$ (ANS)

b). Width of 1st bright fringe on either side of central bright fringe is

  

where y₂ is calculated using the relation,

   $sin \theta_2= \frac{2 \lambda}{a}= \frac{2(633 \times 10^{-9})}{0.405 \times 10^{-3}}$

$\theta_2= 0.179^\circ$

thus, $y_2= d tan\theta_2= 3.30tan(0.179^\circ)= 0.01030m= 10.30mm$

Then width of 1st bright fringe on either side of central bright fringe will be

$w_1= y_2-y_1= (10.30-5.15)mm= 5.15 mm= 5.15 \times 10^{-3}m$ (ANS)